Problem : you want to use the speed/velocity of a layer's movement in space to drive, say, an effect

Solution : If you want to take the speed for a layer's postionnal value, you can use the following expression

position.speed/3 -50

This expression has the advantage of using the speed information coming from a layer's position and applying it to whatever parameter you want it to influence.
For example, if you are moving a layer through a comp, and want the speed of the movement to influence the brightness of the layer, you would just copy and paste this expression to the "Brightness and Contrast" filter, in the Brightness parameter.

Why the /3-50?

Simply because the speed of the layer's position is expressed in 100's (i.e the speed can go from 0 pixels/s to a quite large amount), whereas the brightness goes from 0 to 100. So if you divide the values for speed by 3, you arrive to a decent value for brightness (the brightness won't be overblown).
The -50 adds more control to this, putting the brigthness down by 50. You could change this for any other number, depending on your needs, but you could also not use it and divide the speed by 5, or more.